Resumen de On a nonabelian Kneser theorem

Oriol Serra, Maximilian Wötzel

• The well known theorem of Kneser, stating that small sumsets in abelian groups mustbe periodic, does not hold in nonabelian groups. We prove that in a finite nonabeliangroup G, a weaker version of Kneser’s theorem does hold, stating that if a symmetric set1 ∈ S = S−1 ⊂ G satisfies |S2| < 2|S| − 1 then S2is almost periodic. This is shown in themore general context of vertex transitive graphs. Perhaps surprisingly, the correspondingstatement for infinite vertex transitive graphs turns out to be false.